Yes! Customers with recurring memberships can book past their next payment date, into their next interval (i.e. month), as long as the customer is set to incur another payment. This includes memberships with a "pending activation" status - as long as the membership is projected to be active for the class date, customers can make reservations into the next payment interval.
If the customer's membership expires and will not incur another payment, they cannot book outside their current interval. Additionally, unused usages do not roll over into the next interval.
Example: Niki has a 20 class/mo recurring membership that renews on the 4th. She can book classes on the 5th, 6th, 7th, etc, as long as she is set to incur a payment on the 4th. If she does not have another payment on the 4th, any unused classes that go unused during her current payment interval (month) will not roll over past the 4th and she will be unable to book classes past the 4th.
Customers cannot make reservations past their membership expiration date if the booking window is longer than the non-renewing membership.